Borrowing Constraints and the Tenure Choice of Young Households

Transcription

1 Borrowing Constraints Journal and of the Housing Tenure Research Choice of Young Volume Households 8, Issue Fannie Mae Foundation All Rights Reserved. Borrowing Constraints and the Tenure Choice of Young Households Donald R. Haurin, Patric H. Hendershott, and Susan M. Wachter* Abstract We analyze factors that affect the tenure choice of young adults, highlighting the impact of lenderimposed borrowing constraints. The data set is a panel of youth ages 20 to 33 for 1985 to Our methods differ from those of most prior studies, including consideration of possible sample selection bias, a richer model of the stochastic error structure, better measurement of which households are bound by borrowing constraints, and fuller consideration of the endogeneity of wealth and income. We find ownership tendencies to be quite sensitive to potential earnings, the cost of owning relative to renting, and especially borrowing constraints. In our sample, 37 percent of households are constrained even after choosing their loan-to-value ratio to minimize the impact of the separate wealth and income requirements. The constraints reduce the probability of ownership by 10 to 20 percentage points. Keywords: affordability; homeownership; down payment Introduction Tenure choice has been conventionally viewed as determined by three factors: permanent income, the cost of owning relative to renting, and household life-cycle attributes (Rosen 1985). Permanent income (both long-term earning capacity and income from nonhuman capital), rather than current income, is important because tenure choice and housing consumption are long-term decisions. 1 A series of articles published in 1989 added lender borrowing constraints as a determinant (Jones 1989; Linneman and Wachter 1989; Zorn 1989). Owing to information asymmetries and moral hazard, lenders base borrowing capacity on measurable current income and liquid assets rather than future income and total wealth. Liquid assets are important because lenders require equity contributions from borrowers. The importance of liquid wealth for a down payment is conceptually distinct from its effect through permanent income or total wealth inclusive of human capital. Whether the liquid wealth constraint is an important factor in tenure choice, * Donald R. Haurin is Professor of Economics and Finance at the Ohio State University. Patric H. Hendershott is Galbreath Professor of Real Estate, Max Fisher School of Business, Ohio State University, and Director of Housing and Real Estate Finance Research, Price Waterhouse. Susan M. Wachter is Professor of Real Estate and Finance, the Wharton School, University of Pennsylvania. The authors thank Daniel Feenberg of the National Bureau of Economic Research for his assistance with the TAXSIM program. Research assistance was supplied by Min-Seok Yang and Woo Hyung Yang. 1 Transaction costs, including high search and information costs, and the difficulty of incrementally changing consumption prevent households from adjusting housing quantity instantaneously in response to changing demand (Muth and Goodman 1989).

2 138 Donald R. Haurin, Patric H. Hendershott, and Susan M. Wachter separate from permanent income, must be empirically determined. That these factors are distinct, however, is conceptually clear. In this article we analyze the factors that affect the tenure choice of young adults, extending earlier work to include intertemporal data. We focus on the group making the transition to homeownership; the data set is a panel of youth ages 20 to 33 for the years 1985 to The issue of constraints is likely to be far more relevant for these households than for established older households. Our methods differ from those of most prior studies, including consideration of possible sample selection bias, a richer model of the stochastic error structure, better measurement of which households are bound by borrowing constraints, and a fuller consideration of the endogeneity of wealth and income. Recent Studies Linneman and Wachter (hereafter L-W) used microdata to quantify the impact of income and wealth constraint measures on individual homeownership propensities. The measures were based on the requirements for mortgages that qualify for purchase by Fannie Mae and Freddie Mac, which set industry standards. L-W first estimated the value of the desired house by using a sample of unconstrained homeowners, defined as those having purchased a home with a value less than 85 percent of the maximum allowed by both the income and wealth constraints. They then used the coefficients estimated from the sample of unconstrained owners to calculate desired house value for the rest of their sample (V*). Knowing a household s current income, wealth, and desired house purchase price enabled L-W to measure the extent by which the desired purchase price exceeded the maximum allowed under industry borrowing standards. L-W s method uses six constraint measures: three each for income and wealth. For wealth (W), two dummy variables indicate whether the household is highly constrained or moderately constrained. The maximum house purchase price V W allowable under the wealth constraint is defined as V W = W/(1 LTV*), (1) where LTV* is the maximum loan-to-value ratio allowed by lenders. If the desired house value is greater than V W, the household is defined as highly wealth constrained. If the desired house value is between 90 and 100 percent of V W, the household is moderately wealth constrained. That is, Wealth Gap: High = 1if V W V*, 0 otherwise, and Wealth Gap: Moderate = 1if V W > V* 0.9V W, 0 otherwise. (2) (3)

3 Borrowing Constraints and the Tenure Choice of Young Households 139 The third variable is the dollar difference between the desired and constrained house values for highly constrained households: Wealth Gap: $ Shortage = (V* V W ) (Wealth Gap: High). (4) The expected signs of the coefficients of all three variables when entered into the tenure choice equation are negative. The three income constraints are similarly defined. The maximum house purchase price V I allowable under the current income (y) constraint is V I = (0.28y)/(rLTV*), (5) where r is the interest rate and the 0.28 reflects the lender constraint that the loan payment cannot exceed 28 percent of income (the loan payment is interest only). Two dummy variables (Income Gap: High and Income Gap: Moderate) and a continuous variable (Income Gap: $ Shortage) are defined in the same way as for the wealth constraints. L-W set LTV* equal to 0.8. L-W estimated the probability of homeownership for recent movers by using data from two periods: 1975 to 1979 and 1981 to To provide a baseline for comparison with traditional specifications, they also estimated the model excluding borrowing constraint variables. Including borrowing constraints markedly improved the fit of the model for both sample periods and substantially reduced the estimated impact of household income and age. The wealth constraint variables had larger impacts than the income variables. L-W s research indicated that even in well-developed capital markets, the presence of borrowing constraints, particularly the wealth constraint, negatively affects homeownership propensities. Zorn (1989) tested a model of tenure choice based on utility maximization over three options: maintaining current housing, moving to an owned residence, or moving to rental housing. He used data on 4,000 households surveyed in May 1986 by the Joint Center for Housing Studies. 2 Rather than treating the income and wealth constraints separately, Zorn measured the extent to which the constraints bind as the difference between the desired house value and the minimum value allowed under the more binding of the two constraints, again assuming an 80 percent LTV. Because borrowing constraints limit the quantity of housing that households are able to acquire as owners, Zorn argued that the tenure decision is driven not by the traditional ratio of the costs of owning and renting but by an assessment of the level of utility attainable from the overall consumption bundle of housing and nonhousing goods selected under each tenure alternative. His data supported the hypothesis that movement to owned housing is less likely than the other options when estimated household income and wealth constraints bind. Hendershott, LaFayette, and Haurin (1997) allow households to select the LTV and mortgage product that minimize the impact of the constraint. 3 To illustrate the LTV 2 See Duca and Rosenthal (1994) for a similar analysis. 3 They define the amount of wealth available for a down payment as total wealth less one month of salary, pension investments, consumer durables, closing costs, and mortgage points. This approach suggests that

4 140 Donald R. Haurin, Patric H. Hendershott, and Susan M. Wachter decision, for most households the impact is minimized by selecting the LTV that equates the two constraint values. Equating V W from equation (1) and V I from equation (5) yields LTV* = 0.28y/(0.28y + rw). (6) Hendershott, LaFayette, and Haurin find that allowing for mortgage and LTV choice reduces by about a third the fraction of recently moving households estimated to be constrained. The potential importance of wealth to tenure choice has also been considered by Jones (1989). Using a Canadian data set, he finds that current net worth plays a far more important role than human capital in triggering first-time homeownership. A model highlighting the importance of current wealth argues that if the lender-imposed wealth constraint is unavoidable in the mortgage market, then all new homeowners will have current net wealth sufficient to make the down payment on their purchased house. Also, if ownership is the desired tenure choice for all households and only the wealth constraint prohibits some from owning, then all renters will have wealth less than that required by the constraint. Thus, the outcome of a comparison of current wealth with the minimum required to meet the lending constraint for the desired house will predict homeownership perfectly. However, current wealth is not an exogenous variable in a household s multiperiod choice of whether or when to become a homeowner. Rather, annual savings decisions determine wealth, and saving is partly determined by a household s choice of labor supply and expenditures (other factors include wage rates, gifts, and inheritances). In fact, the desire to become a homeowner is likely a major determinant of wealth accumulation among youth (Haurin, Hendershott, and Wachter 1997). 4 This argument suggests that tests of the importance of mortgage lender constraints on tenure choice must allow wealth and the indicator of whether the wealth constraint is binding to be endogenous, whereas Jones treated wealth as exogenous. 5 Because ownership intentions are influenced by the household s ability to save, cross-sectional data are not likely to enable an analyst to sort out the causal structure between saving and homeownership. The availability of intertemporal data should allow a better understanding of this link. Data and Statistical Model Our primary data set is the National Longitudinal Survey of Youth (NLSY), housed at the Center for Human Resource Research at the Ohio State University. Although the data have been collected annually since 1979, wealth was not reported until The survey has an excellent retention rate (90 percent or higher). The NLS Handbook (Center for Human Resource Research 1991) reports the method of data collection. Respondents L-W s moderate wealth constraint indicator equals unity when a household is constrained by available wealth, assuming that 10 percent of wealth is described by the list of alternative uses. 4 There are other reasons for wealth accumulation. Housing assets are part of a household s portfolio of wealth holdings. The optimal portfolio likely includes other types of assets (Grossman and Laroque 1990; Pissarides 1978). Plaut (1987) notes that uncertain house prices create a demand for financial assets. 5 Similar comments apply to current income and the lender-imposed income constraint.

5 Borrowing Constraints and the Tenure Choice of Young Households 141 were ages 14 to 21 in 1979; thus, our study from 1985 to 1990 includes youth ages 20 to 32, this being the age range when many people are saving toward their first home purchase. A detailed description of the data set is contained in our earlier article (Haurin, Hendershott, and Wachter 1996). 6 In that study, we tested the reliability of the wealth data by comparing them with data from the Survey of Consumer Finances and found the two sets to be similar. Also, we compared the reported homeownership rates in the NLSY with those in the American Housing Survey and again found good agreement. Other variables in our study have been tested and found to be reliable; these reports are summarized in the earlier article. The means of variables used in our study are listed in table 1. All nominal data are deflated. Table 1. Means of Variables Variable Mean Variable Mean Permanent income a 2.23 Ownership rate 0.18 Relative cost of owning 0.98 Family size 2.72 Expected length of tenancy Respondent test score 4.19 Income gap: high 0.17 House value a 5.41 c Income gap: moderate 0.04 Respondent male 0.44 Income gap: $ shortage a 0.20 Respondent bad health 0.03 Wealth gap: high 0.64 House price index 8.45 Wealth gap: moderate 0.03 Parents education Wealth gap: $ shortage a 1.40 Log owner cost 8.80 Gifts from relatives 0.22 Respondent wage 6.26 Black 0.32 Spouse wage 7.21 b Hispanic 0.17 Central city 0.28 Respondent age Suburbs 0.30 Spouse age b In other part of MSA 0.39 Married 0.37 Northeast 0.19 Years married 3.43 b North Central 0.35 Respondent highest grade completed West 0.20 Spouse highest grade completed b a Tens of thousands of dollars. b Mean for married respondents. c Mean for homeowners. 6 We use the full NLSY sample, unweighted. The justification for this choice is discussed in the NLS Handbook (Center for Human Resource Research 1991, 50).

6 142 Donald R. Haurin, Patric H. Hendershott, and Susan M. Wachter One positive aspect of the panel data is that the intertemporal consistency of a respondent s data can be checked, and outliers can be identified and deleted or corrected if other corroborative information is present. The resulting data set is superior to a single cross section in terms of accuracy of measurement. Another positive aspect is that respondentspecific unobserved variables can be taken into account in the error structure of the econometric model. An important variable not present in the NLSY is the cost of constant-quality housing. This measure is a component of the owner cost of housing and the relative owner-renter cost. We use the Fannie Mae Freddie Mac repeat sales house price index for metropolitan statistical areas (MSAs) because it has wide spatial coverage and is available for 1985 to This series has good correlation with other series such as those of Coldwell Banker (see Haurin, Hendershott, and Kim 1991) and the American Chamber of Commerce (see Haurin, Hendershott, and Wachter 1996). Because the Fannie Mae Freddie Mac repeat sales series is an index, we need a single cross section of house prices to obtain house price levels; we use the 1987 American Chamber of Commerce data (ACCRA 1987). Tenure Choice and Lender Constraints We reconsider and extend the L-W method of analysis of the impact of lender constraints on tenure choice. The extensions include better measurement of desired house value, the use of exogenous proxies for permanent income, the treatment of wealth as endogenous, allowance for endogenous LTV choice, and a superior econometric technique. Below, we discuss each modification. Desired House Value To measure the constraint variables, we must measure the value of the house that would be purchased if there were no mortgage lender constraints. L-W s measurement technique uses a sample restricted to unconstrained owners to estimate desired house value for all households. But if this unconstrained sample is selective, the resulting estimation of desired house value will not be applicable to constrained homeowners and renters. For example, it is possible that the sample of unconstrained owners consists of households that have a taste for atypically small houses. The desired house value should be derived by a method that corrects for possible sample selection bias, such as the Heckman (1979) two-step correction technique. We applied the Heckman method to our longitudinal sample and found no evidence of sample selection bias. 7 Thus our method of deriving the desired house value is an ordinary least squares regression of the logarithm of house value on a set of household characteristics and the cost of owned housing using a sample of unconstrained owners. The results are reported in the first numeric column of table A.1. Explanatory variables replicate the L-W set and include age, marriage, family size, gender, race/ethnicity, 7 The first step of the procedure is to estimate a probit model of which households are included in the sample of unconstrained owners. Unconstrained owners house value is less than 85 percent of the maximum allowed by both constraints. From this estimation, an inverse Mills ratio (l) is created and inserted into the housing demand equation. The significance level of l is only 0.3; thus there is no evidence of selection bias in this sample.

7 Borrowing Constraints and the Tenure Choice of Young Households 143 permanent income, central-city location, suburban location, whether in an MSA, three regional variables, and the logarithm of the owner cost of housing. Permanent income and the owner cost of housing are based on standard formulations (Goodman and Kawai 1982; Hendershott and Shilling 1982). 8 In the estimation of desired house value, we find that the most significant factors are permanent income, age, race/ethnicity, marriage, central-city location, and regional location. Permanent Income and Wages The concept of permanent income is valid only if labor supply is fixed (Killingsworth 1983). For youth, this assumption is not appropriate. Thus we replace permanent income with a measure of the wage a youth could earn if employed full time (potential wage), this variable being independent of other endogenous choices such as labor supply or living arrangement (Haurin, Hendershott, and Kim 1994). We predict wages separately for respondent and spouse (if present). The sample cannot be limited to youth working full time because of the possibility of selection bias. We found that estimation results best conform to expectations when we use a Tobit model on the full sample. Censored observations include all youth not working at least 30 hours per week. Explanatory variables include age, highest grade completed, an achievement test score, gender, race/ ethnicity, and health. For the respondent, all variables are significant at the 0.05 level except for education level squared and age (table A.1). The most significant are the achievement test score, gender, and race/ethnicity. The results for spouses are not as good, but the sample of positive wage observations is much smaller. Endogenous Wealth The wealth and constraint variables should be treated as endogenous to allow for youth simultaneously determining tenure status and savings. This modification requires that a two-stage least squares approach be used to create an instrumental variable for wealth. Our longitudinal data set allows us to test a random effects model that allows for autocorrelation. For household i at time t, the model is W it = b9z it + y i + e it, (7) e it = re i,t 1 + h it, (8) 8 L-W use the human capital model of Goodman and Kawai (1982) to determine permanent income. Explanatory variables include highest grade completed, age of head of household, family size, and the squares of these three terms. Also included are dummy variables for head being male or black. We replicate their approach except that our estimation allows for a random household-specific stochastic error in our panel data. All coefficients except the one for family size are significant and have the expected sign. The owner cost is [(1 t y)r + d + (1 t y )t p p e ]p h h, where p h h is the local real constant-quality house price index, r is the interest rate, d is the depreciation and maintenance rate, t y is the marginal income tax rate, t p is the local property tax rate, and p e is expected house price inflation. The source of house prices was described previously, interest rates fell from in 1985 to in 1990, depreciation and maintenance equal annually, and expected house price inflation is Property taxes vary by state, and the marginal tax rate is calculated by the National Bureau of Economic Research TAXSIM program for the years 1985 to 1990 (Feenberg 1993).

8 144 Donald R. Haurin, Patric H. Hendershott, and Susan M. Wachter E(y i ) = 0, Var(y i ) = s y 2, Cov(e it, y i ) = 0, (9) Var(e it + y i ) = s 2 = s y 2 + s e 2, Corr(e it + y i, e is + y i ) = s y 2 /s 2. (10) In equation (7), wealth is a function of the explanatory variables Z, a household-specific random error y i, and a random error e it that varies over households and time. This error term e it is allowed to be autocorrelated as described in equation (8), where the autocorrelation coefficient is r and h it is a stochastic error that varies over households and time. Variances of the errors are represented by s. The estimation method is generalized least squares. 9 Results of the wealth estimation are reported in the last column of table A.1. Because this is a reduced-form equation, it is not appropriate to give structural interpretations to the coefficients. Identification is achieved by inclusion of a number of variables, such as the total number of years in current marriage, dollar amount of gifts from relatives, and parental education level (highest grade completed by either parent). A Lagrange multiplier test of this model versus the alternative of a nonautocorrelated classical regression model yields a Lagrange multipler statistic of 1,802, this being highly significant. The intertemporal correlation of household-specific residuals is estimated to be The autocorrelation r in equation (8) is only The predicted value of wealth derived from this estimation is then used in the derivation of the constraint variables described in equations (2) and (3). Measurement of the Income and Wealth Constraints The L-W method yields a total of six measures of the tightness of the lender-imposed income and wealth constraints. We reduce the number of variables to three by taking into account a household s optimal adjustment to the income and wealth constraints. As explained by Hendershott, LaFayette, and Haurin (1997), a household falls into one of three categories: It is unconstrained by the lender requirements regarding current income and wealth, constrained by one of the two requirements, or constrained by both. If bound by only one constraint when the LTV is 0.8, a household will move away from the 0.8 LTV to loosen the binding constraint even though this action tightens the nonbinding constraint. LTV is modified until one of three cases occurs: The household is constrained by neither requirement, both constraints are equally binding in terms of how much housing can be purchased, or the household faces a limiting case such as being unable to obtain a loan with a down payment less than 5 percent. In the first case, the constraints are zero. In the other two cases, we determine the optimal LTV by finding the value that makes the constraints equally binding with the requirement that LTV be no greater than 0.95 (see equation (6)). In these cases, some households that were judged highly constrained by L-W s method become moderately constrained, some that were judged moderately constrained become unconstrained, and the measure of the wealth or income shortfall decreases. We report the percentage of constrained households in table 2. L-W s reported percentages of constrained households depend on the time period. For 1981 to 1983, they find 9 The method is described in detail in the LIMDEP manual (Greene 1994, ).

9 Borrowing Constraints and the Tenure Choice of Young Households 145 Table 2. Percentage of Households Constrained by Mortgage Lender Income and Wealth Requirements L-W H-H-W H-H-W Constraint Income gap: high Wealth gap: high Minimized gap: high 37 Income gap: moderate 6 4 Wealth gap: moderate 1 5 Minimized gap: moderate 6 Note: L-W is Linneman and Wachter (1989); H-H-W is this study. that 27 percent of households are highly income constrained and 40 percent are highly wealth constrained; 6 and 1 percent, respectively, are moderately constrained. When we replicate L-W s method and definitions of the constraints, we find that the percentage of highly income constrained households is nearly identical (28 percent), but the percentage of highly wealth constrained households is much higher (58 percent), as expected given our younger sample. About 5 percent of young households are moderately constrained. When households select the optimal LTV, we expect the most binding constraint to be loosened. This expectation is confirmed because the average LTV rises to 0.85, resulting in only 37 percent of households being highly constrained by either income or wealth. 10 Moderately constrained households now equal 6 percent of the sample. Model of Tenure Choice The equation for tendency to own a home is assumed to have the following general form: O it = b X 9X it + m i + n it, (11) where m i is a household-specific stochastic error and n it is a random error that varies over households and time. The explanatory variables included in X are potential wage, cost of owning relative to renting, race/ethnicity, family size, marital status, expected length of tenancy, and a vector of wealth- and income-based mortgage constraint measures. 11 We 10 Wealth continues to be the (slightly) more binding constraint, the evidence being that after LTV optimization, only 30 percent of households face a binding income constraint, while 37 percent face a binding wealth constraint. This difference occurs because 7 percent of households reach the maximal LTV allowed (0.95). As expected, there are no households constrained only by income after the LTV is optimized. 11 The correct measure of the cost of owning relative to renting is the ratio of owner costs to renter costs. The owner cost measure differs from that used in the estimation of housing demand because the marginal tax rate is replaced by the tenure choice tax rate (Hendershott and Slemrod 1983). The tenure choice tax rates were calculated with NBER s TAXSIM program. Our rental cost variable is from Coldwell Banker, and it measures the rental cost of a constant-quality dwelling unit in a large number of MSAs. However, the Coldwell Banker sample of MSAs is smaller than the Fannie Mae Freddie Mac house price sample, so using the relative cost variable reduces sample size by 25 percent. Estimation using the larger sample and owner costs (based on the tenure choice tax rate) produces results very similar to estimates based on the smaller sample using the relative cost of owning. We report results from the larger sample because most of the variation in the relative price is due to variation in real house price, not in rents (Capozza, Green, and Hendershott 1996).

10 146 Donald R. Haurin, Patric H. Hendershott, and Susan M. Wachter do not observe the tendency to own; rather, we observe the result of the discrete choice of whether to own or rent. The justification for inclusion of the relative cost and the constraint measures is provided in the appendix. The error structure in the tendency-to-own equation is a generalization of the typical cross-sectional approach, and it contains the usual random component and a personspecific random error m i. The complete error structure is Var( i + it ) Var( it )= 2 + 2, (12) Corr 2 ( it, is ) 2 = ( + ). (13) The likelihood function and details of the estimation are described by Butler and Moffitt (1982). 12 A significant r indicates that the household-specific stochastic errors are correlated over time, in which case a simple probit approach applied to the entire panel of data would be inappropriate. This structure addresses the problem of unobserved heterogeneity that results from omitted variables, an approach possible only with a panel data set. Results Our first task is to replicate the estimation method and variables of L-W, thus confirming their original study and deriving a baseline against which to compare the new results. Although our source of data differs from L-W s, most of their explanatory variables are available or can be created from the NLSY. The dependent variable is an indicator of whether the respondent is a homeowner. L-W s explanatory variables are demographic (black, Hispanic, family size, married, and age of head) and economic (permanent income, cost of owning relative to renting, expected duration of tenancy, and a series of indicators of mortgage lender constraints). 13 Differences between our baseline case and L-W s method include our use of a longitudinal data set rather than a cross section, our use of probit rather than logit, and our treatment of age as continuous given the limited age range of our respondents rather than splitting age of head into seven categories. Initially, although our sample is longitudinal, we simply pool the data and ignore intertemporal correlation of household-specific residuals. Given that the data sets cover different periods and contain different ages of household head (ours is limited to young adults, while L-W include the entire age spectrum), it would not be surprising if the estimation results differed. The comparison of L-W s outcomes for the and periods with our results is reported in table 3, where we find substantial similarity. Whenever an economic variable is significant for L-W, it is significant in our estimation, and in a few cases we find that additional coefficients are significant and have the sign predicted by theory. Coefficients of some demographic 12 The advantage of their model is that it is relatively easy to estimate. The disadvantage is that the correlation is the same from period to period. 13 We create expected length of tenancy by L-W s method.

11 Borrowing Constraints and the Tenure Choice of Young Households 147 variables differ (e.g., family size and black), perhaps because of the much lower average age in our sample. A comparison of the key elasticities of ownership tendencies also yields the conclusion that our baseline findings are similar to those of L-W when their method is replicated. For example, L-W estimate the elasticity of homeownership with respect to the relative cost of owning to be 0.93, compared with our estimate of Estimates of the elasticity of ownership with respect to permanent income are 0.37 and 0.31, respectively. We conclude that using L-W s method on a different data set yields generally similar findings. Table 3. Signs and Significance of Coefficients for Linneman-Wachter and Haurin- Hendershott-Wachter Tenure Choice Estimation Results H-H-W L-W L-W Variable Predicted Baseline Case Permanent income + + +** +* Relative cost of owning *** *** Expected length of tenancy + + +*** Income gap: high *** ** ** Income gap: moderate *** * Income gap: $ shortage + Wealth gap: high *** ** *** Wealth gap: moderate *** *** Wealth gap: $ shortage + *** *** Black +** Hispanic + Head age + + a + a Married + +*** +* +*** Family size + +*** + a L-W include a series of seven age range dummy variables. In general, ownership tendencies rise as age increases, and if a single variable had been used, it would likely have been statistically significant. *p < 0.1. **p < ***p < We next make the improvements discussed previously and determine whether any of the baseline results change. Table 4 lists our baseline estimates in the first column of results. 14 In the next column, we replace income with two wage variables, we replace the six constraint variables with three, and we replace observed wealth with an instrumental variable; however, we do not impose the random effects model of the stochastic errors. We find significant effects for respondent s and spouse s potential wages, the relative cost of owning, indicators of whether the household is highly or moderately constrained, and marriage. All these coefficients have the expected signs. 14 We do not list L-W s results because logit specifications yield coefficients that differ from those of probit models, although marginal effects can be compared.

12 148 Donald R. Haurin, Patric H. Hendershott, and Susan M. Wachter Table 4. Probit Estimation Results of Homeownership Tendencies Variable Baseline Extended Model Random Effects a Constant 1.51 (5.3) 1.62 (6.4) 4.95 (10.0) Permanent income b 0.17 (1.7) Respondent wage 0.08 (4.2) 0.18 (4.4) Spouse wage 0.06 (3.0) 0.09 (2.0) Relative cost of owning b 1.45 (10.5) 1.27 (10.5) 3.02 (11.4) Expected length of tenancy 0.21 (3.8) 0.04 (0.7) 0.23 (2.4) Income gap: high 0.33 (1.9) Income gap: moderate 0.28 (1.6) Income gap: $ shortage b 0.04 (0.5) Wealth gap: high 1.17 (12.1) Wealth gap: moderate 0.99 (5.9) Wealth gap: $ shortage b 0.11 (3.5) Minimized gap: high 0.54 (4.9) 0.38 (2.5) Minimized gap: moderate 0.47 (3.6) 0.55 (3.3) Minimized gap: $ shortage b 0.01 (0.2) 0.13 (0.2) Black 0.28 (2.0) 0.17 (1.4) 0.14 (0.6) Hispanic 0.12 (1.6) 0.06 (0.8) 0.17 (0.8) Head age 0.02 (0.7) 0.03 (1.5) 0.07 (1.9) Married 0.56 (6.5) 0.41 (3.5) 0.63 (2.9) Family size 0.03 (1.5) 0.01 (0.9) 0.02 (0.7) r 0.73 (14.0) Sample size 4,206 4,206 4,206 Log-likelihood 1,201 1,517 1,199 Significance level <0.001 <0.001 <0.001 Note: Figures in parentheses are t statistics. a This model treats wealth, and thus the constraint variables, as endogenous; it includes random indvidual effects. b Tens of thousands of dollars. In the final column, we report the results of the random effects estimation, where we find that the estimate of period-to-period error correlation is 0.73 and is highly significant. 15 Thus, we find evidence of omitted variables in the tenure choice estimation. Lender constraints reduce the probability of owning for both highly and moderately constrained households. The coefficient of the variable indicating that the household is highly constrained is only one-third that of the separate wealth constraint variable 15 The x 2 test of the reduction in log-likelihood yields a value of 637. With one degree of freedom, this is significant at the level.

13 Borrowing Constraints and the Tenure Choice of Young Households 149 ( 0.38 versus 1.17), but it is slightly greater in absolute value than that of the income constraint ( 0.38 versus 0.33). A similar pattern holds for moderately constrained households. The impact of being highly constrained on the probability of ownership depends on the values of the other explanatory variables. Our example is for a 30-year-old white married couple with one child having average values for wages, relative cost of owning, and expected length of tenancy. The probability of owning a home is 0.20 if the household is unconstrained and falls to about 0.10 if it is constrained. If wages equal $10 hourly for both respondent and spouse rather than the mean of about $7, the probability of owning is 0.52 if unconstrained and 0.34 if constrained. 16 We find that the variable measuring the real dollar amount of the housing shortfall created by the lender constraints (i.e., the strength of the lender constraint) has no significant separate impact on the tenure decision. Rather, the two dummy variables measuring whether a household is highly or moderately constrained explain the total impact. Other significant explanatory variables in the random effects model include the relative cost of owning, respondent s and spouse s wage rates, expected length of tenancy, and marriage. Increased expected length of tenancy results in a reduced annualized expected transaction cost of selling, and we confirm that the likelihood of ownership increases. Marriage also raises the probability of homeownership, even when household wealth and potential wages are controlled. We find no effect of family size or race/ethnicity. Increased age has a marginally significant positive effect on the tendency to own a home. 17 We note that the random effects approach changes many coefficient values compared with the case where r is constrained to be zero (the extended model). Coefficients for respondent s wage and age double, that of marriage increases by 50 percent, that of spouse s wage rises by 40 percent, that of expected length of tenancy rises by a factor of 6, that of relative cost rises in absolute value by 140 percent, and that for the highly constrained indicator falls by 30 percent. In our preferred model, elasticity estimates of the ownership tendency are 0.5 with respect to wages, 1.4 for relative costs, 0.5 for expected length of tenancy, and 0.9 for age. As noted above, if borrowing requirements are binding, the tendency to own is substantially reduced. Conclusions Three 1989 articles provided the first evidence that lender-imposed borrowing constraints adversely affect homeownership propensities. Our study builds on these articles by using a data set restricted to young households, the group most likely to be constrained, and making a number of improvements to their methods. We find that borrowing constraints significantly reduce the tendency toward ownership. 16 If wages for both equal $8.30 hourly, the predicted probability of ownership is 0.35 if unconstrained, the same as the sample mean in the L-W study. If the household is constrained, the probability of ownership falls to 0.21, a 40 percent reduction. In contrast, L-W report that highly constrained households (in either income or wealth) were 20 percent less likely to own, implying a reduction in ownership rates from 0.35 to If the three constraint variables are omitted from the estimation, the Hispanic coefficient nearly doubles, the coefficients of the wage variables rise by 20 percent, and other coefficients are within 10 percent of the values in the last column of table 4.

14 150 Donald R. Haurin, Patric H. Hendershott, and Susan M. Wachter Our methods differ from prior studies in five ways. First, because household saving is clearly a choice variable for young households (Haurin, Hendershott, and Wachter 1997), household wealth is determined simultaneously with tenure choice. We use an instrumental variable approach to address this concern, endogenizing our measure of borrowing constraint severity. Second, we consider the problem of sample selection bias in the estimation of a household s desired amount of housing, this being an input to the borrowing constraint measures. However, we find no evidence of selection bias in our sample. Third, we reject the use of permanent income in the tenure choice equation because income depends on labor supply, which is clearly jointly determined (Haurin, Hendershott, and Kim 1994). Instead, we use an estimate of wages earned if employed full time and find that increases in either respondent s or spouse s wages raise the propensity to become a homeowner. Fourth, our sample is a panel data set. Panel data allow us to estimate a richer error structure in which we test for household-specific random errors that are correlated over time. We find that the correlation of errors is highly significant and large, Allowing for this correlation has a substantial impact on explanatory variables coefficients in the tenure choice model, generally increasing their size. Fifth, we allow households to minimize the impact of income and wealth constraints by optimizing LTV (Hendershott, LaFayette, and Haurin 1997). This change substantially reduces the estimated number of households facing a binding constraint. Our first step in the estimation is to replicate L-W s results, but with a sample of younger households. In spite of this difference in data, similar results are obtained if a similar estimation method is used. This finding allows us to identify differences resulting from the five changes in estimation technique. In our preferred model, we find that the tendency toward homeownership is sensitive to a household s earning capacity as measured by wage rates. Ownership propensities also depend on the cost of owning relative to renting, age, marital status, and the expected length of tenancy. Compared with those of L-W, our estimates of the responsiveness of ownership to these variables are larger and generally have a higher level of statistical significance. We highlight the question of whether binding borrowing constraints influence homeownership probabilities. We find that if a household is constrained or very nearly constrained because of low current income or wealth, then its probability of owning is substantially reduced. The reduction depends on the values of other explanatory variables. We give two examples: If the unconstrained probability of owning is 0.2, the imposition of a borrowing constraint reduces the likelihood of owning by half. If the unconstrained probability is 0.5, the reduction in probability of owning is a third. An interesting finding is that if a household faces a binding constraint, there is no additional effect on the tendency to own if the shortfall in current wealth or income is increased. Our results suggest that marginally constrained households are no more likely to own than severely constrained households, implying that households do not seek smaller properties to reduce the impact of lender constraints. We suggest that more research is needed into whether youth facing binding lender constraints reduce their desired property size. If such a response does not occur, the policy implication is that intervention to reduce the severity of the constraint faced by households will not affect homeownership unless the intervention eliminates the constraint.

15 Borrowing Constraints and the Tenure Choice of Young Households 151 Appendix Table A.1. Estimation of Household Desired House Value, Wage, and Wealth Log of Log of Respondent Log of Spouse Variable House Value Wage: Tobit Wage: Tobit Wealth Constant 5.69 (3.5) (0.8) Respondent male 0.10 (1.5) 0.43 (18.0) 2.14 (3.1) 3.73 (3.3) Respondent black 0.26 (2.4) 0.25 (8.2) 0.10 (1.3) (2.8) Respondent Hispanic 0.27 (3.2) 0.12 (3.6) 0.17 (2.3) 0.78 (0.5) Married 0.24 (2.2) (4.3) Years married 1.24 (4.9) Gifts from relatives 0.99 (8.1) House price index 0.07 (0.4) Parents education 0.20 (1.2) Respondent highest grade 0.09 (2.0) 3.38 (4.3) Respondent age 0.23 (3.7) 0.04 (1.5) 0.76 (0.5) Respondent test score* 0.21 (12.3) 1.02 (1.4) Respondent bad health indicator 0.24 (3.5) 0.30 (0.2) Spouse highest grade 0.15 (2.4) 0.71 (3.1) Spouse age 0.08 (2.2) 0.50 (4.4) Respondent age squared (3.9) (2.9) 0.60 (1.9) Respondent test score* squared 0.02 (10.3) 0.08 (1.2) Respondent highest grade squared (0.7) Spouse age squared (1.1) Spouse highest grade squared (0.8) Interaction variables Respondent highest grade respondent age squared 0.01 (5.5) Black respondent male 1.07 (0.5) Black respondent age 1.19 (0.3) Black respondent highest grade 0.28 (0.5) Black respondent test score* 0.34 (0.6) Black spouse age 0.08 (0.3) Black spouse highest grade 0.58 (1.3) Black house price 0.11 (0.3) Log owner cost 0.04 (0.3) Family size 0.01 (0.4) Permanent income 0.09 (8.0) Central city 0.47 (2.7) Suburbs 0.23 (1.3) In other part of MSA 0.22 (1.3) Northeast 0.22 (2.3) North Central 0.04 (0.5) West 0.18 (2.0) Sample size 500 4,206 4,206 4,206 R *Achievement test score in tens.

16 152 Donald R. Haurin, Patric H. Hendershott, and Susan M. Wachter Dougherty and Van Order (1982) derive an expression for the owner cost of housing when a household faces a binding wealth constraint. Their expression is [(1 t y )r + d + (1 t y )t p p e + α]p h h, where all variables have been previously defined except α, which is the ratio of the shadow price of the mortgage lender s constraint to the marginal utility of the composite consumption good. Their extended owner cost expression is additively separable into the standard owner cost term and αp h h. Our econometric model includes the standard owner cost and the Gap: $ Shortage variable, measured as p h (h* h W ), where h* is the amount of housing demanded if the household does not face a lender s constraint and h W is the maximal amount of housing that can be purchased subject to the down payment constraint. The question addressed in this appendix is the relationship of p h (h* h W ) to αp h h. Assume that a household maximizes utility subject to the usual income constraint and a wealth constraint uw > p h h/r, where u = 1/(1 LTV) > 1 (house rents are capitalized at rate r): Max U(x, h) + l y (y x p h h) + l W (uw p h h/r), (A.1) where y is income, x is nonhousing consumption with a price set to unity, and l y and l W are the Lagrangian multipliers. Upon simplification, the first-order conditions are y = U x (A.2) and U h W = r U x p h. (A.3) From Dougherty and Van Order s 1982 definition of the additional term in the user cost expression, p h h = W U h p U x h h = rh U x p h. (A.4) Our continuous measure of the wealth constraint is Gap: $ Shortage = p h (h* h W ). If constrained, the consumption of housing is h W = urw/p h. Thus, the change in our measure of the constraint with respect to wealth is Gap/ W = r. (A.5) For Dougherty and Van Order, the change in their variable measuring the constraint with respect to wealth is more easily seen if a specific form is assumed for the utility function. If utility is Cobb-Douglas, where U = h d x 1 d, then equation (A.4) becomes

17 Borrowing Constraints and the Tenure Choice of Young Households 153 p h h = r (l ) x p h h. (A.6) If constrained, then ]h/]w = ur/p h and ]x/]w = ur, the latter derived from the income constraint. Thus, we find the response to a change in wealth is ( p h h)/ W = r2 l. (A.7) Comparing equations (A.5) and (A.7), Gap/ W = ( p h h)/ W. (A.8) r (l ) Thus, our measure of the strength of the constraint varies directly with the expression given by Dougherty and Van Order. That is, Dougherty and Van Order s derivation provides a theoretical basis for including the Gap variable in the tenure choice equation along with the standard user cost variable. References ACCRA (formerly American Chamber of Commerce Researchers Association) Cost of Living Index. Louisville, KY. Butler, J. S., and Robert Moffitt A Computationally Efficient Quadrature Procedure for the One Factor Multinomial Probit Model. Econometrica 50(3): Capozza, Dennis, Richard Green, and Patric H. Hendershott Taxes, Mortgage Borrowing, and Residential Land Prices. In The Economic Effects of Fundamental Tax Reform, ed. Henry J. Aaron and William G. Gale, Washington, DC: Brookings Institution Press. Center for Human Resource Research NLS Handbook. Columbus: Ohio State University. Dougherty, Ann, and Robert Van Order Inflation, Housing Costs, and the Consumer Price Index. American Economic Review 72(1): Duca, John, and Stuart Rosenthal Borrowing Constraints and Access to Owner-Occupied Housing. Regional Science and Urban Economics 24: Feenberg, Daniel Richard, and Elizabeth Coutts An Introduction to the TAXSIM Model. Journal of Policy Analysis and Management 12(1): Goodman, Allen, and Masahiro Kawai Permanent Income, Hedonic Prices, and Demand for Housing: New Evidence. Journal of Urban Economics 12: Greene, William LIMDEP Reference Manual, Version 6.0. Chicago: LIMDEP. Grossman, Sanford J., and Guy Laroque Asset Pricing and Optimal Portfolio Choice in the Presence of Illiquid Durable Consumption Goods. Econometrica 58(1):25 51.

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